Hydrocarbon fluids, e.g. oil and natural gas, are obtained from a subterranean geologic formation, referred to as a reservoir, by drilling a well that penetrates the hydrocarbon-bearing formation. Once a wellbore is drilled, various forms of well completion components may be installed to control and enhance the efficiency of producing fluids from the reservoir. For example, various types of valves, e.g. subsurface safety valves, may be installed as part of the well completion. In many subsurface safety valves, a flow tube is moved in a longitudinal direction to open a flapper or to allow the flapper to close. Movement of the flow tube in the opening direction is resisted by a spring member that tends to take substantial space and/or increase the overall length of the valve.